Zinc-finger proteins of the Cys2His2 type bind DNA-RNA hybrids with affinities comparable to those for DNA duplexes. Such zinc-finger proteins were converted into site-specific cleaving enzymes by fusing them to the FokI cleavage domain. The fusion proteins are active and under optimal conditions cleave DNA duplexes in a sequence-specific manner. These fusions also exhibit site-specific cleavage of the DNA strand within DNA-RNA hybrids albeit at a lower efficiency (approximately 50-fold) compared to the cleavage of the DNA duplexes. These engineered endonucleases represent the first of their kind in terms of their DNA-RNA cleavage properties, and they may have important biological applications.